A loose or bad connection anywhere in the circuit, switch, fixture, lamp socket, and can be either of the two wires of the circuit.
Can be a defective lamp socket or switch.

Using a voltage tester, begin at the switch. Be sure there is power feeding the switch, then check if there is power leaving the switch. If this is all fine, then need to check the connections at and in the fixture.

It can be as simple as the bottom contact of the lamp socket is pushed down too far and the bottom contact of the lamp cannot reach the lamp. Be sure the power is off, as this contact is the hot, and gently pull or pry the contact up a fraction of an inch.

I have a ceiling light fixture that works only rarely--once in 3-4 weeks.

What could be possible causes?

I think there's an excellent chance that there is a loose connection between two wires where they connect in the ceiling box. Another possibility is that the lamp socket (the part the bulb screws into) is cracked. This often happens when people install bulbs of too high a wattage rating.

You can look on the fixture and it should say somewhere what the maximum wattage rating for that fixture is. If you have exceeded it (e.g. 150 Watt bulb in a socket rated for 60 Watts) or if you see any cracks or burn marks then you should replace it because it is probably damaged internally and is now a fire hazard.

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